This paper introduces DONUT-hole, a sparse OCR-free visual document understanding (VDU) model that addresses the limitations of its predecessor model, dubbed DONUT. The DONUT model, leveraging a transformer architecture, overcoming the challenges of separate optical character recognition (OCR) and visual semantic understanding (VSU) components. However, its deployment in production environments and edge devices is hindered by high memory and computational demands, particularly in large-scale request services. To overcome these challenges, we propose an optimization strategy based on knowledge distillation and model pruning. Our paradigm to produce DONUT-hole, reduces the model denisty by 54\% while preserving performance. We also achieve a global representational similarity index between DONUT and DONUT-hole based on centered kernel alignment (CKA) metric of 0.79. Moreover, we evaluate the effectiveness of DONUT-hole in the document image key information extraction (KIE) task, highlighting its potential for developing more efficient VDU systems for logistic companies.